Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2017  FebMar  (P19709/12)  Q#7
Question
The function f is defined for by .
i. Find and .
The first, second and third terms of a geometric progression are respectively , and .
ii. Find the value of the constant k.
Solution
i.
We are given the function;
Therefore;
Rule for differentiation of is:
Therefore;
Second derivative is the derivative of the derivative. If we have derivative of the curve as , then expression for the second derivative of the curve is;
Rule for differentiation of is:
ii.
We are given that the first, second and third terms of a geometric progression are respectively , and .
Let’s find first three terms of the Geometric Progression (G.P).
























Hence, first three terms of the Geometric Progression (G.P).
Expression for Common Ratio () in a Geometric Progression (G.P) is;








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